QuestionSolve the inequality and express the solution in interval notation.
Studdy Solution
STEP 1
Assumptions1. The inequality is . We are looking for the values of that satisfy this inequality3. The solution should be written in interval notation
STEP 2
First, we can factor out the common factor from the inequality.
STEP 3
Now, we need to find the critical points of the inequality. These are the values of that make the expression equal to zero.
To find the critical points, we set each factor equal to zero and solve for .
STEP 4
olving the above equations gives us the critical points.
STEP 5
Now, we need to test the intervals determined by the critical points to see where the inequality is greater than zero.
The intervals are , , and .
STEP 6
Choose a test point in the interval , say , and substitute it into the factored inequality.
STEP 7
Calculate the result of the inequality with the test point .
This is true, so the interval is part of the solution.
STEP 8
Choose a test point in the interval , say , and substitute it into the factored inequality.
STEP 9
Calculate the result of the inequality with the test point .
This is false, so the interval is not part of the solution.
STEP 10
Choose a test point in the interval , say , and substitute it into the factored inequality.
STEP 11
Calculate the result of the inequality with the test point .
This is true, so the interval is part of the solution.
STEP 12
Combine the solution intervals to write the final solution in interval notation.
The solution to the inequality is .
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